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On a nonlocal differential equation describing roots of polynomials under differentiation

Abstract: In this work we study the nonlocal transport equation derived recently by Steinerberger [Proc. Amer. Math. Soc., 147(11):4733{4744, 2019]. When this equation is considered on the real line, it describes how the distribution of roots of a polynomial behaves under iterated di erentiation of the function. This equation can also be seen as a nonlocal fast di usion equation. In particular, we study the well-posedness of the equation, establish some qualitative properties of the solution and give conditions ensuring the global existence of both weak and strong solutions. Finally, we present a link between the equation obtained by Steinerberger and a one-dimensional model of the surface quasi-geostrophic equation used by Chae et al. [Adv. Math., 194(1):203{223, 2005].

Otras publicaciones de la misma revista o congreso con autores/as de la Universidad de Cantabria

 Fuente: Communications in Mathematical Sciences. Vol. 18, No. 6, pp. 1643-1660

Editorial: International Press

 Año de publicación: 2020

Nº de páginas: 18

Tipo de publicación: Artículo de Revista

ISSN: 1539-6746,1945-0796

Proyecto español: MTM2017-89976-P

Url de la publicación: https://dx.doi.org/10.4310/CMS.2020.v18.n6.a6